Cryptography

## Cipher

Cryptography

A cipher is defined over the spaces of: All Keys, $$\mathscr{K}$$ All Messages, $$\mathscr{M}$$ All Cipher texts, $$\mathscr{C}$$ Cipher (defined as a triple, $$(\mathscr{K}, \mathscr{M}, \mathscr{C})$$) as a pair of algorithms $$(\mathbf{E}, \mathbf{D})$$ where $$\mathbf{E}$$ represents the encryption algorithm and $$\mathbf{D}$$ represents the decryption algorithm. $$\mathbf{E}: \mathscr{K} \times \mathscr{M} \rightarrow \mathscr{C}$$ and $$\mathbf{D}: \mathscr{K} \times \mathscr{C} \rightarrow \mathscr{M}$$ Such that: $$\forall m \in \mathscr{M}, k \in \mathscr{K}: \mathbf{D}(k, \mathbf{E}(k, m)) = m$$ ...

## Distribution Vector

A vector with non-negative components (representing specific probabilities) which add up to one e.g. $$(P(x_{0}), P(x_{1}),…,P(x_{n}))$$ Also known as: Stochastic Vector

## Uniform Distribution

$$x \in U:P(x) = \frac{1}{|U|}$$ Where $$|U|$$ is the size of the universe (set). In Probability Theory, a uniform distribution assigns an equal probability to each element of a given set.

## Point Distribution

x0: P(x) = 1,∀ x ≠ x0: P(x) = 0 In Probability Theory, a point distribution is a distribution which assigns all the probability to a given point (set element).

## Cryptography

Cryptography

Digital Signature

## Digital Signature

Cryptography

A function of the content being “signed”